trunk with mass of 200 kig on ramp with 45 degree angle with the horizontal. Ramp covered with ice and frictionless. Find acceleration of trunk as slides down.
To find the acceleration of the trunk as it slides down the ramp, we can use the principles of Newtonian mechanics.
The force acting on the trunk can be resolved into two components: the force of gravity and the normal force provided by the ramp. The force of gravity can in turn be resolved into two components: the component parallel to the ramp (F_parallel) and the component perpendicular to the ramp (F_perpendicular).
First, we need to find the component of gravity parallel to the ramp. We can do this by multiplying the mass of the trunk (200 kg) by the acceleration due to gravity (9.8 m/s^2) and taking the sine of the angle of the ramp (45 degrees):
F_parallel = m * g * sin(θ)
F_parallel = 200 kg * 9.8 m/s^2 * sin(45°)
Next, we need to find the net force acting on the trunk. Because the ramp is frictionless, there is no horizontal force acting on the trunk except F_parallel. Therefore, the net force acting on the trunk will be equal to F_parallel:
F_net = F_parallel
Finally, we can calculate the acceleration of the trunk using Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
F_net = m * a
By equating the above equations, we can find the acceleration:
F_parallel = m * a
Substituting the values we already calculated, we get:
200 kg * 9.8 m/s^2 * sin(45°) = 200 kg * a
Simplifying further, we have:
a = 9.8 m/s^2 * sin(45°)
a ≈ 6.93 m/s^2
Therefore, the acceleration of the trunk as it slides down the ramp would be approximately 6.93 m/s^2.