Physics

3 Free Body Diagram

Need in 2–3 hour

Question 1
A person pulls a crate with 120 N of force against 100 N of friction a distance of 5 meters. Sketch a free body diagram showing the forces acting on the crate and find the energy the person expends pulling the crate, the amount of energy converted to heat via friction, and the increase in the kinetic energy of the crate. Please show your step-by-step solution along with formulas.

SOLUTION:

Work done by person= Force applied by the person * distance travelled by the crate

= 120N * 5m = 600N/m2

Work done by friction = force against friction * distance travelled by the crate

= 100N * 5m = 500N/m2
Increase in kinetic energy = (120 – 100) N * 5m = 20 * 5 = 100 joules.

Question 2
A box of mass 4 kg is resting on a table 1.5 m above the floor. There is also a ledge located 5 m above the floor. First, provide a sketch of this problem. Then, find the gravitational potential energy of the box relative to the floor, and the gravitational potential energy of the box relative to the ledge. Please show your step-by-step solution along with formulas.

SOLUTION: Ep_floor = mgh

= 4kg * 9.8m/s² * 1.5m

= 58.8 joules
Ep_ledge = mgh

= 4kg * 9.8m/s² * (-3.5m)

= – 137.2 joules

Question 3
An 80 kg man climbs a 50 m-high hill in 20 minutes. What is the average power in watts he expends climbing the hill? Please show your step-by-step solution along with formulas.

SOLUTION: Power = Work / time

= mgh / t

= 80kg * 9.8m/s² * 50m / 1200s

= 32.7 W

Question 4
A 40,000 kg railroad car initially traveling at 10 m/s collides in-elastically with a 20,000 kg railroad car initially at rest. The cars stick together. What is their final speed? Please show your step-by-step solution along with formulas.

SOLUTION: Initial momentum: p = mv

= 40000kg * 10m/s

= 400 000 kg·m/s

Final momentum: p = 400 000 kg·m/s = 60000kg * v
v = 6.7 m/s

Question 5
A roller coaster is initially at a height of 40 m above the ground and has an initial velocity of 15 m/s. Using conservation of energy, find the velocity of the roller coaster at a height of 5 m above the ground. Sketch the problem before you solve it. Please show your step-by-step solution along with formulas.

SOLUTION: Initially E = Ep + Ek = mgh + ½mv² = M * 9.8m/s² * 40m + ½M * (15m/s)²
E = 392M + 112.5M = 504.5M
Later, E = 504.5M = M * 9.8 * 5 + ½Mv² = M(49 + ½v²)
M cancels:
504.5 = 49 + ½v²
v² = 2(504.5 – 49) = 911
v = 30.2 m/s