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A tree is steadied by three cables as shown. Each cable carries a tension of 1.5 kN. Determine the position
vector, unit vector and force vector for each cable acting on the tree.Estimate the direction angles of cable
AB. Calculate the direction angles and direction cosines of cable AB.

A mast is restrained by three cables as shown. The tension in cable CE is 2 kN. Estimate the angle between cables CE and CD. Use the dot product to determine the angle between cables CE and CD. Write force vector F (CE). Determine the projection of F (CE) in the direction of CD. Express the projection as a vector.

The spring has an unstretched length of 14 in. and a stiffness of 80 lb/ft. Determine the height x corresponding to static equilibrium in the position shown. Determine the tension in the diagonal cable.

A weather balloon is tethered by the lines AB, AC, and AD. The mass of the balloon and the gas it contains is 80 kg, and the (upward) buoyancy force on the balloon is 1000 N. Draw a free body diagram of particle A. Write force vectors in terms of their unknown tensions. Estimate the tensions in lines AB, AC, and AD. Set up the equilibrium equations and solve for the unknown tension in each line.

The turnbuckle shown is tightened until the tension in cable AB equals 2.4 kN. Determine the moment about point O due to cable AB using position vector r (OA). Determine the moment about point O due to cable AB using position vector r (OB). How does this result compare with that of part a? Determine the moment about point D due to cable AB.

Cable AB exerts a force of 1.2 kN on the lever as shown. Calculate the moment about bar OC using the moment about O. Calculate the moment about bar OC using the moment about C. Calculate the moment about line OD. Calculate the moment about line OA.

An angled bracket is loaded as shown. Calculate the equivalent force-couple system acting at point O. At what point along the x-axis would a single-force equivalent act? If the point of application of the couple were moved to point B, what effect would this have on the magnitude, direction, and application of the single-force equivalent?

The given beam is loaded as shown. Note the triangular loading at the end of the beam is in the upward direction. Replace the distributed loading on the beam with an equivalent set of point loads and identify the location and direction of each of the point loads. Combine the set of point loads into a single equivalent point load and determine the point of application along the beam.

A mast is restrained by three cables as shown. The tension in cable CE is 2 kN. Estimate the angle between cables CE and CD. Use the dot product to determine the angle between cables CE and CD. Write force vector F (CE). Determine the projection of F (CE) in the direction of CD. Express the projection as a vector.

The spring has an unstretched length of 14 in. and a stiffness of 80 lb/ft. Determine the height x corresponding to static equilibrium in the position shown. Determine the tension in the diagonal cable.

A weather balloon is tethered by the lines AB, AC, and AD. The mass of the balloon and the gas it contains is 80 kg, and the (upward) buoyancy force on the balloon is 1000 N. Draw a free body diagram of particle A. Write force vectors in terms of their unknown tensions. Estimate the tensions in lines AB, AC, and AD. Set up the equilibrium equations and solve for the unknown tension in each line.

The turnbuckle shown is tightened until the tension in cable AB equals 2.4 kN. Determine the moment about point O due to cable AB using position vector r (OA). Determine the moment about point O due to cable AB using position vector r (OB). How does this result compare with that of part a? Determine the moment about point D due to cable AB.

Cable AB exerts a force of 1.2 kN on the lever as shown. Calculate the moment about bar OC using the moment about O. Calculate the moment about bar OC using the moment about C. Calculate the moment about line OD. Calculate the moment about line OA.

An angled bracket is loaded as shown. Calculate the equivalent force-couple system acting at point O. At what point along the x-axis would a single-force equivalent act? If the point of application of the couple were moved to point B, what effect would this have on the magnitude, direction, and application of the single-force equivalent?

The given beam is loaded as shown. Note the triangular loading at the end of the beam is in the upward direction. Replace the distributed loading on the beam with an equivalent set of point loads and identify the location and direction of each of the point loads. Combine the set of point loads into a single equivalent point load and determine the point of application along the beam.

Beam AB is loaded with a 2 kN force and a 2.4 kN-m couple as shown. Draw a free body diagram of beam AB.
Determine the reactions at the supports. If the reaction at roller B was found to be negative, what would
this imply physically about the system?

A pair of pliers grips the bolt as shown below. For an input force, P = 40 N, determine the force exerted on the bolt. Draw free body diagrams of the upper handle, the lower handle, and the jaw (link CDE). Determine the forces in the link AB and determine the force exerted on the bolt at point E.

What are the components of the reactions at the wall? Find the value of the distributed load and take the moment about point A.

Find the y-component of the centroid for the case below. All dimensions are in inches and the area of the region is 18 in squared. y=9-2x^2

What is the maximum load, W, that can be pulled-up (lifted) by the application of 200-lb on the rope? A weight is pulled up from a rope wrapped around a stationary pulley.

Determine the center of mass in the x-direction for the thin rod provided below. Assume that it has a constant mass per unit length of 4 slugs/ft.

Determine the equivalent force and the point of application for the hydrostatic pressure applied to the 1 ft (out of the paper) wide wall.

A 250 lb refrigerator is on a surface with a coefficient of friction of 0.6 . A tension, T, is applied to a rope that is wrapped around a pulley with a coefficient of friction of 0.5 . Draw a free body diagram of the refrigerator for the case of impending tipping. Use the figure provided below. Solve for the tension, T, for the refrigerator to tip. Draw the free body diagram of the refrigerator for the case of impending slipping. Use the figure provided below. Solve for the tension, T, for the refrigerator to slip. Will the refrigerator tip or slip?

A pair of pliers grips the bolt as shown below. For an input force, P = 40 N, determine the force exerted on the bolt. Draw free body diagrams of the upper handle, the lower handle, and the jaw (link CDE). Determine the forces in the link AB and determine the force exerted on the bolt at point E.

What are the components of the reactions at the wall? Find the value of the distributed load and take the moment about point A.

Find the y-component of the centroid for the case below. All dimensions are in inches and the area of the region is 18 in squared. y=9-2x^2

What is the maximum load, W, that can be pulled-up (lifted) by the application of 200-lb on the rope? A weight is pulled up from a rope wrapped around a stationary pulley.

Determine the center of mass in the x-direction for the thin rod provided below. Assume that it has a constant mass per unit length of 4 slugs/ft.

Determine the equivalent force and the point of application for the hydrostatic pressure applied to the 1 ft (out of the paper) wide wall.

A 250 lb refrigerator is on a surface with a coefficient of friction of 0.6 . A tension, T, is applied to a rope that is wrapped around a pulley with a coefficient of friction of 0.5 . Draw a free body diagram of the refrigerator for the case of impending tipping. Use the figure provided below. Solve for the tension, T, for the refrigerator to tip. Draw the free body diagram of the refrigerator for the case of impending slipping. Use the figure provided below. Solve for the tension, T, for the refrigerator to slip. Will the refrigerator tip or slip?

A truss is supported at joints J and D, as shown. The length of each strut in the structure is 8 m. Complete
the free body diagram of the structure proved below. Determine the reactions at points J and D. Determine
the loads carried by member CG, GD, and GF using appropriate free body diagrams to motivate your equations.

An ideal (frictionless) pulley A supports block B of mass m. The cable is wrapped over a rough, stationary drum, as shown. Determine the maximum mass, m, for which the system will remain stationary. Determine the minimum mass, m, for which the system will remain stationary.

Determine the y-component of the centroid for the region shown below. y=1+x^3/6

Determine the x-component of the centroid for the object shown below. Find the centroid of the triangle with a cirlcle cut through it.

The mechanism shown below holds back a column of water with height h= 3 m using a gate pinned at point A. You may assume that the bottom of the gate just touches the ground, but that the ground exerts negligible force on it. The density of water is 1000 kg/m^3. Determine the force that the water exerts on the gate and its location. Draw a free body diagram of the gate. Determine the load carried by member BC.

Tower OD is supported with 3 cables DA, DB, and DC. If the tension in cable DC is 20 kN, write a vector expression for the force in cable DC. The force in cable DB is given by T = 2.29 i - 9.73 k kN. Determine the magnitude of the projection of T in the direction of DC.

Curved bar ABCD is loaded with a single force as shown. Determine the equivalent force-couple system at point A.

Telephone pole ABC is partially supported by cable CD. If the tension in cable CD is 10 kN, determine the moment about point A due to this cable.

Angled bar ACB is supported by a pin at A and a roller reaction at B. The bar is loaded with a 4000 Nm couple as shown. Draw a complete free body diagram of bar ACB. Determine the magnitude of the reaction force at the roller support at B. Determine the magnitudes of the reactions at pin A. If the 4000 Nm applied moment were shifted to the end of the angled bar, would the magnitude of N increase, decrease, or remain the same?

Truss A-L is supported with a fixed support at joint A and a roller support at joint I. the truss is loaded with two forces as whon and is in static equilibrium. Determine the magnitudes of the support reactions at joints A and I. Determine the loads in members EF and FK. Also, identify whether these members are in tension or compression. Identify all zero-force members in the truss. Pick one zero-force member and prove it's a zero-force member using your equilibrium equations.

An ideal (frictionless) pulley A supports block B of mass m. The cable is wrapped over a rough, stationary drum, as shown. Determine the maximum mass, m, for which the system will remain stationary. Determine the minimum mass, m, for which the system will remain stationary.

Determine the y-component of the centroid for the region shown below. y=1+x^3/6

Determine the x-component of the centroid for the object shown below. Find the centroid of the triangle with a cirlcle cut through it.

The mechanism shown below holds back a column of water with height h= 3 m using a gate pinned at point A. You may assume that the bottom of the gate just touches the ground, but that the ground exerts negligible force on it. The density of water is 1000 kg/m^3. Determine the force that the water exerts on the gate and its location. Draw a free body diagram of the gate. Determine the load carried by member BC.

Tower OD is supported with 3 cables DA, DB, and DC. If the tension in cable DC is 20 kN, write a vector expression for the force in cable DC. The force in cable DB is given by T = 2.29 i - 9.73 k kN. Determine the magnitude of the projection of T in the direction of DC.

Curved bar ABCD is loaded with a single force as shown. Determine the equivalent force-couple system at point A.

Telephone pole ABC is partially supported by cable CD. If the tension in cable CD is 10 kN, determine the moment about point A due to this cable.

Angled bar ACB is supported by a pin at A and a roller reaction at B. The bar is loaded with a 4000 Nm couple as shown. Draw a complete free body diagram of bar ACB. Determine the magnitude of the reaction force at the roller support at B. Determine the magnitudes of the reactions at pin A. If the 4000 Nm applied moment were shifted to the end of the angled bar, would the magnitude of N increase, decrease, or remain the same?

Truss A-L is supported with a fixed support at joint A and a roller support at joint I. the truss is loaded with two forces as whon and is in static equilibrium. Determine the magnitudes of the support reactions at joints A and I. Determine the loads in members EF and FK. Also, identify whether these members are in tension or compression. Identify all zero-force members in the truss. Pick one zero-force member and prove it's a zero-force member using your equilibrium equations.

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