A 4-person bobsled team pushes the 330 kg sled down the 6.0 degree hill with a force of 1780 N. The coefficient of friction for ice and the runner is 0.135. How fast will the sled be moving at the end of the 40m push? Answer is in meters/second
M*g = 330 * 9.8 = 3234 N. = Wt. of sled.
Fp = 3234*sin6 = 38 N. = Force parallel
to the incline.
Fn = 3234*Cos6 = 3216 N. = Normal = Force perpendicular to the incline.
Fk = u*Fn = 0.135 * 3216 = 434.2 N. = Force of kinetic friction.
a = (Fap-Fk)/M = (1780-434)/330 = 4.08 m/s^2
V^2 = Vo^2 + 2a*d
Vo = 0
a = 4.08 m/s^2
d = 40 m.
Solve for V.
To find the speed of the sled at the end of the 40m push, we can use the principle of work-energy.
First, let's find the work done by the pushing force. Work is equal to the force applied multiplied by the distance over which it is applied. In this case, the force is 1780 N and the distance is 40 m.
Work (W) = Force (F) × Distance (d)
W = 1780 N × 40 m
W = 71200 N·m
Next, we need to find the total work done on the sled, taking into account the work done by the pushing force and the work done against friction.
The work done against friction can be calculated by multiplying the coefficient of friction (μ) by the normal force (N) and the distance (d). The normal force is equal to the weight of the sled, which can be found by multiplying the mass (m) by the acceleration due to gravity (g).
Normal force (N) = mass (m) × acceleration due to gravity (g)
N = 330 kg × 9.8 m/s²
N = 3234 N
Work against friction (Wf) = coefficient of friction (μ) × Normal force (N) × Distance (d)
Wf = 0.135 × 3234 N × 40 m
Wf = 17417.4 N·m
Now, let's find the net work done on the sled. Net work (Wnet) is the difference between the work done by the pushing force and the work done against friction.
Wnet = Work by pushing force (W) - Work against friction (Wf)
Wnet = 71200 N·m - 17417.4 N·m
Wnet = 53782.6 N·m
The net work done on the sled is equal to the change in kinetic energy of the sled. So we can equate the net work to the change in kinetic energy:
Wnet = ΔKE
The change in kinetic energy (ΔKE) can be calculated using the equation:
ΔKE = (1/2) × mass (m) × final velocity squared (vf²) - (1/2) × mass (m) × initial velocity squared (vi²)
Since the sled starts from rest, the initial velocity is 0.
ΔKE = (1/2) × mass (m) × final velocity squared (vf²)
Now we can rearrange the equation to solve for the final velocity (vf):
vf² = (2 × ΔKE) / mass (m)
vf = √((2 × ΔKE) / mass (m))
Substituting the values we have:
vf = √((2 × 53782.6 N·m) / 330 kg)
Simplifying:
vf = √(32549832 N·m) /√(330 kg)
vf = √(98695.52 N) /√(330 kg)
vf ≈ 10.5 m/s
Therefore, the sled will be moving at approximately 10.5 meters/second at the end of the 40m push.