A 1500 kg car accelerates from rest under the actions of two forces. One is a forward force of
1260 N provided by traction between the wheels and the road. The other is a 870 N resistive
force due to various frictional forces. Use the work-energy theorem to determine how far the
car must travel for its speed to reach 9.5 m/s.
Ummm don't understand. Is this correct?
1/2[1500][9.5]=[1260-870]cos[d]
nope, not right.
final Ke+workdoneonfrciton=force*distance
1/2 m vf^2+870*d=1260*d
1/2 m vf^2=distance*(1260-870)
1/2 *1500*9.5^2)/390=distance
I think that will be the same answer that I gave you before.
To determine how far the car must travel for its speed to reach 9.5 m/s using the work-energy theorem, we need to consider the following:
1. Calculate the net force acting on the car:
The net force is equal to the forward force provided by traction minus the resistive force due to friction.
Net force = Forward force - Resistive force
Net force = 1260 N - 870 N
Net force = 390 N
2. Determine the work done by the net force:
Work = Force × Distance × cos(θ)
Since the car accelerates in the same direction as the net force, the angle (θ) between the force and displacement is 0 degrees. Therefore, cos(0) = 1.
Work = Net force × Distance × cos(0)
Work = 390 N × Distance × 1
Work = 390 N × Distance
3. Apply the work-energy theorem:
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy.
Work = ΔKE (Change in kinetic energy)
Since the car starts from rest (zero initial velocity), the initial kinetic energy (KE1) is zero.
ΔKE = KE2 - KE1
ΔKE = 1/2 × mass × (final velocity)^2 - 1/2 × mass × (initial velocity)^2
ΔKE = 1/2 × 1500 kg × (9.5 m/s)^2 - 1/2 × 1500 kg × (0 m/s)^2
ΔKE = 1/2 × 1500 kg × (9.5 m/s)^2
Now we equate the work done to the change in kinetic energy and solve for the distance:
390 N × Distance = 1/2 × 1500 kg × (9.5 m/s)^2
Now we can solve for the distance:
Distance = (1/2 × 1500 kg × (9.5 m/s)^2) / 390 N
By evaluating this equation, we can determine how far the car must travel for its speed to reach 9.5 m/s.