Physics: Find Wagon Speed Up 18.1° Hill Given Tension and Distance

[marishik]

A 32,1 kg wagon is towed up a hill inclined at 18.1 degrees with respect to the horizontal. The two rope is parallel to the incline and has a tension of 114N in it. Assume that the wagon starts from rest at the bottom of the hill and neglet friction. The acceleration of gravity is 9.8m/s2. How fast is the wagin going after moving 62.5m up the hill? Answer in units of m/s

 

[Päällikkö]

Please show what you've tried.

 

[quicknote]

To find the speed of the wagon, we can use the equation for the component of acceleration in the direction of the incline:

a = g*sin(18.1) = 9.8*sin(18.1) = 2.9 m/s^2

Next, we can use the equation for acceleration in terms of force and mass:

a = F/m

Substituting in the given values, we get:

2.9 m/s^2 = 114N/32.1kg

Solving for the mass, we get:

m = 114N/2.9 m/s^2 = 39.3 kg

Now, we can use the equation for velocity in terms of acceleration, distance, and initial velocity:

v^2 = u^2 + 2as

Where u is the initial velocity (which is 0 since the wagon starts from rest) and s is the distance traveled (62.5m).

Substituting in the values, we get:

v^2 = 0 + 2*2.9 m/s^2*62.5m = 362.5 m^2/s^2

Taking the square root of both sides, we get:

v = √(362.5 m^2/s^2) = 19.04 m/s

Therefore, the wagon is moving at a speed of 19.04 m/s after moving 62.5m up the hill.