Question

Consider a wooden ramp angled 34.6 degrees above horizontal. If a 7.55-kg wooden block is given a strong shove up the ramp so that it has an initial velocity of 27.8 m/s, how long (in seconds) will it take the block to reach its maximum height (before it starts sliding down)? The coefficient of kinetic friction between the block and the ramp is 0.403.

Answer 1

To find the time it takes for the block to reach its maximum height, you need to consider the components of the block's initial velocity that are parallel and perpendicular to the ramp. Use the equation of motion and the force of kinetic friction to calculate the time.

Step-by-step explanation:

To find the time it takes for the block to reach its maximum height, we need to consider the components of the block's initial velocity that are parallel and perpendicular to the ramp. The component of the initial velocity parallel to the ramp will eventually be negated by the force of kinetic friction, causing the block to come to a stop. The component of the initial velocity perpendicular to the ramp will determine the block's upward motion. We can use the equations of motion to find the time it takes for the block to reach its maximum height.

First, we need to find the component of the initial velocity parallel to the ramp. Vparallel = Vinitial * sin(angle)
Vparallel = 27.8 m/s * sin(34.6°) = 15.3 m/s

Next, we need to find the time it takes for the block to come to a stop. The force of kinetic friction is given by Ffriction = coefficient * normal force. The normal force can be calculated using the equation normal force = mass * gravity * cos(angle). Using the equation Ffriction = mass * acceleration, we can find the acceleration due to kinetic friction, acceleration = Ffriction / mass.

Finally, we can use the equation of motion V = Vinitial + (acceleration * time) to find the time it takes for the block to come to a stop. Rearranging this equation gives us time = (V - Vinitial) / acceleration.

So the total time it takes for the block to reach its maximum height is time total = 2 * time because it will take the same amount of time for the block to come to a stop and then reverse its motion. Plug in the values and calculate the time.