A 3.00 kg block starts from rest at the top of a 36.0'> incline and slides 2.00 m down the incline in 1.60 s.
(a) Find the acceleration of the block.
m/s2
(b) Find the coefficient of kinetic friction between the block and the incline.
(c) Find the frictional force acting on the block.
N
(d) Find the speed of the block after it has slid 2.00 m.
m/s
acceleration=changevelocity/time= 2avgvel/time
average velocity= distance/time
B) you know final velocity(2*avg velocity)
Hmmm. I don't see how it can be done without slope.
To find the acceleration of the block, you can use the following equation:
acceleration = (final velocity - initial velocity) / time
In this case, the block starts from rest, so the initial velocity is 0 m/s. The final velocity can be determined using the distance and time traveled.
First, let's calculate the final velocity. The distance traveled down the incline is given as 2.00 m, and the time taken is given as 1.60 s.
distance = 2.00 m
time = 1.60 s
Using the formula:
final velocity = distance / time
final velocity = 2.00 m / 1.60 s = 1.25 m/s
Now, we can calculate the acceleration:
acceleration = (final velocity - initial velocity) / time
acceleration = (1.25 m/s - 0 m/s) / 1.60 s
acceleration = 1.25 m/s / 1.60 s
acceleration ≈ 0.781 m/s^2
Therefore, the acceleration of the block is approximately 0.781 m/s^2.
To find the coefficient of kinetic friction between the block and the incline, we need to use the equation:
frictional force = coefficient of friction * normal force
where the normal force is the force exerted by the incline on the block perpendicular to the incline.
First, let's calculate the normal force. The weight of the block, which acts vertically downward, can be determined by multiplying its mass (3.00 kg) by the acceleration due to gravity (9.8 m/s^2).
weight = mass * acceleration due to gravity
weight = 3.00 kg * 9.8 m/s^2
weight ≈ 29.4 N
Since the incline is at an angle of 36°, the normal force can be determined by calculating the vertical component of the weight. The normal force is equal in magnitude but opposite in direction to the weight's vertical component.
normal force = weight * cos(angle of incline)
normal force = 29.4 N * cos(36°)
normal force ≈ 23.5 N
Now, we can determine the frictional force by solving for the coefficient of kinetic friction:
frictional force = coefficient of friction * normal force
The frictional force can be calculated using the equation:
frictional force = mass * acceleration
However, in this case, the block is moving, so we can substitute the mass times acceleration with the product of the mass and acceleration determined earlier.
frictional force = mass * acceleration
frictional force = 3.00 kg * 0.781 m/s^2
frictional force = 2.343 N
Therefore, the frictional force acting on the block is approximately 2.343 N.
To find the speed of the block after it has slid 2.00 m, we can use the equation:
final velocity^2 = initial velocity^2 + 2 * acceleration * distance
Since the block starts from rest, the initial velocity is 0 m/s.
final velocity^2 = 0 m/s + 2 * 0.781 m/s^2 * 2.00 m
final velocity^2 = 3.124 m^2/s^2
Taking the square root of both sides:
final velocity = sqrt(3.124 m^2/s^2)
final velocity ≈ 1.77 m/s
Therefore, the speed of the block after it has slid 2.00 m is approximately 1.77 m/s.