Homework #3 Solutions
Physics 221 Summer 2012
HOMEWORK #3
Due Monday July 2, 2012
1
James Bond (90 kg), outfitted with perfectly matching skis and skiware, is at the top of a steep slope that a secret spy like him can easily handle. He lets himself go from rest and smoothly slides down the h = 15 m high hill. A big parking lot lies at the bottom of the hill. Since the parking area has been cleared of snow, the friction between the ground and the skis brings our hero to a halt at point D, located at a distance d = 12 m from point C. The descent can be considered frictionless. Take the potential energy to be zero at the bottom of the slope. (a) What is the mechanical energy of James Bond at points A and D? (b) Determine the speed of Bond at position B abd C. (c) What is the work done by friction in the parking lot? (d) Find the magnitude of the average friction force. SOLUTION : (a) At point A EA = mgh = (90 kg) 9.80 m/s2 (15 m) = 13230 J At point B, James Bond is at rest so, EB = 0 (b) Using conservation of energy: EA = EB ⇒ EA = EC ⇒ mgh = mg h 1 + mv 2 ⇒ 2 2 B ⇒ vB = vC = gh = 2gh = 9.80 m/s2 (15 m) = 12.1 m/s 2 9.80 m/s2 (15 m) = 17.1 m/s
1 2 mgh = mvC 2
(c) Using conservation of energy: EC + Wf
C→D
= ED ⇒
Wf
C→D
= ED − EC = -13230 J
where we used the fact that EC = EA . (d) Using the definition of work: Wf = f kd ⇒ fk = Wf
C→D
C→D
d
=
13230 J = 1100 N 12 m
1
Physics 221 Summer 2012
HOMEWORK #3
Due Monday July 2, 2012
2
An object of mass m = 3.00 kg is released from rest at a height of h = 5.00 m on an inclined ramp with angle θ = 10.0◦ with the horizontal. At the foot of the ramp and after a horizontal surface of length d = 20.0 m is the tip of a spring of force constant ik = 4000 N/m (see figure). The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest. Find x and describe what happens to the object after it comes to rest. (a) If all surfaces are frictionless. (b) If
HOMEWORK #3
Due Monday July 2, 2012
1
James Bond (90 kg), outfitted with perfectly matching skis and skiware, is at the top of a steep slope that a secret spy like him can easily handle. He lets himself go from rest and smoothly slides down the h = 15 m high hill. A big parking lot lies at the bottom of the hill. Since the parking area has been cleared of snow, the friction between the ground and the skis brings our hero to a halt at point D, located at a distance d = 12 m from point C. The descent can be considered frictionless. Take the potential energy to be zero at the bottom of the slope. (a) What is the mechanical energy of James Bond at points A and D? (b) Determine the speed of Bond at position B abd C. (c) What is the work done by friction in the parking lot? (d) Find the magnitude of the average friction force. SOLUTION : (a) At point A EA = mgh = (90 kg) 9.80 m/s2 (15 m) = 13230 J At point B, James Bond is at rest so, EB = 0 (b) Using conservation of energy: EA = EB ⇒ EA = EC ⇒ mgh = mg h 1 + mv 2 ⇒ 2 2 B ⇒ vB = vC = gh = 2gh = 9.80 m/s2 (15 m) = 12.1 m/s 2 9.80 m/s2 (15 m) = 17.1 m/s
1 2 mgh = mvC 2
(c) Using conservation of energy: EC + Wf
C→D
= ED ⇒
Wf
C→D
= ED − EC = -13230 J
where we used the fact that EC = EA . (d) Using the definition of work: Wf = f kd ⇒ fk = Wf
C→D
C→D
d
=
13230 J = 1100 N 12 m
1
Physics 221 Summer 2012
HOMEWORK #3
Due Monday July 2, 2012
2
An object of mass m = 3.00 kg is released from rest at a height of h = 5.00 m on an inclined ramp with angle θ = 10.0◦ with the horizontal. At the foot of the ramp and after a horizontal surface of length d = 20.0 m is the tip of a spring of force constant ik = 4000 N/m (see figure). The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest. Find x and describe what happens to the object after it comes to rest. (a) If all surfaces are frictionless. (b) If