A brick of mass 1.0 kg slides down an ice roof inclined at 30 degrees with respect to the horizantal. If the brick starts from rest, how fast is it moving when it reaches the edge of the roof 0.90s later? Ignore friction
force down the plane: mgSinTheta
force=ma solve for a.
then, vf= a*time
To determine the speed of the brick when it reaches the edge of the roof, we can use the principles of kinematics. Let's break down the problem solving process step by step:
Step 1: Determine the acceleration of the brick.
Since the problem states that there is no friction, the only force acting on the brick is its weight. This force can be broken down into two components: one parallel to the incline, and the other perpendicular.
The component parallel to the incline can be determined by multiplying the weight of the brick (mass * acceleration due to gravity) by the sine of the angle of inclination (30 degrees in this case):
F_parallel = m * g * sin(30°)
Using the mass given in the problem (1.0 kg) and the acceleration due to gravity (9.8 m/s^2), we can calculate the parallel force.
Step 2: Calculate the acceleration of the brick.
We know from Newton's second law that acceleration is equal to the net force divided by mass.
a = F_parallel / m
Dividing the parallel force we calculated in step 1 by the mass of the brick will give us the acceleration.
Step 3: Calculate the final velocity of the brick.
We can use the equation of motion for an object sliding down an inclined plane:
v = u + at
Here, v is the final velocity (what we are trying to find), u is the initial velocity (which is zero since the brick starts from rest), a is the acceleration (calculated in step 2), and t is the time taken (0.90 seconds).
Plugging in the values into the equation, we can solve for the final velocity.
Step 4: Calculate the speed.
The final velocity gives us the magnitude and direction of the velocity of the brick. However, since the problem asks for the speed (which is a scalar quantity and refers to the magnitude of velocity only), we need to calculate the magnitude of the final velocity.
Speed = |final velocity|
Taking the absolute value of the final velocity will give us the speed of the brick when it reaches the edge of the roof.
Using these steps, you should be able to solve the problem and find the speed of the brick when it reaches the edge of the roof.