Suppose a hockey puck slides down a frictionless ramp with an acceleration of 4.70 m/s2.
(a)What angle does the ramp make with respect to the horizontal?
(b) If the ramp has a length of 6.40 m, how long does it take the puck to reach the bottom?
(c) Now suppose the mass of the puck is doubled. What's the puck's new acceleration down the ramp?
weight component down ramp = m g sin T
so
m g sin T = m a
4.7 = 9.81 sin T
sin T = .479
T = 28.6 degrees
d = (1/2) a t^2
6.4 = 2.35 t^2
solve for t
LOL - the mass cancels, no difference
To answer these questions, we can use the principles of physics, specifically Newton's second law of motion and the trigonometry of right triangles. Let's go through each question step by step.
(a) To find the angle of the ramp relative to the horizontal, we need to use the formula for the acceleration down an inclined plane. The formula is:
acceleration = g * sin(theta)
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and theta is the angle of the ramp.
Rearranging the formula, we have:
theta = arcsin(acceleration / g)
Plugging in the given acceleration (4.70 m/s^2) and the value of g, we can calculate theta using a scientific calculator or an online tool based on trigonometric functions.
(b) To find the time it takes for the puck to reach the bottom of the ramp, we can use the kinematic equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, the puck starts from rest (initial velocity = 0), and the distance is given as 6.40 m. We can rearrange the equation to solve for time:
time = sqrt((2 * distance) / acceleration)
Plugging in the values, we can calculate the time it takes for the puck to reach the bottom.
(c) To find the new acceleration when the mass of the puck is doubled, we need to consider Newton's second law of motion, which states that force is equal to mass times acceleration (F = m * a). In this case, the force causing the acceleration is the component of the force of gravity parallel to the ramp, which can be calculated as:
force = mass * gravity * sin(theta)
where theta is the angle of the ramp. If we double the mass of the puck, the force will also double, and therefore the acceleration will double as well.
By following these steps, you should be able to find the answers to each part of the question.