1. a force of 250N is used to push a heavy box down the street. If the force of friction between the box and the street is 195N and the box has a mass of 60kg, what is the accleration of the box?
2.a force of 40N is applied to a 6kg box of books. If the frictional force acting on the box is 16N, and the box was initially at rest, what is the velocity of the box 10s later? What is the box's displacement over the 10s period?
F = m a
250 - 195 = 60 a
a = (250-195)/60
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F = 40 - 16 = 24 N
a = F/m = 24/6 = 4 m/s^2
v = a t
v = 4*10 = 40 m/s
average speed over the ten seconds = 20m/s
displacement = 20 t = 200 m
thanks!
1. To find the acceleration of the box, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the net force acting on the box:
Net force = applied force - force of friction
Net force = 250N - 195N
Net force = 55N
Now, we can calculate the acceleration using the formula:
Net force = mass * acceleration
55N = 60kg * acceleration
Rearranging the equation to solve for acceleration, we have:
acceleration = 55N / 60kg
acceleration ≈ 0.92 m/s^2
Therefore, the acceleration of the box is approximately 0.92 m/s^2.
2. To find the velocity of the box after 10 seconds, we can use the equation of motion:
velocity = initial velocity + (acceleration * time)
Given that the box was initially at rest, the initial velocity is 0 m/s. The acceleration can be determined using the same calculation as in question 1 (assuming the applied force is still 40N):
Net force = applied force - force of friction
Net force = 40N - 16N
Net force = 24N
Using Newton's second law of motion:
acceleration = net force / mass
acceleration = 24N / 6kg
acceleration = 4 m/s^2
Now, we can calculate the velocity:
velocity = 0 + (4 m/s^2 * 10s)
velocity = 40 m/s
Therefore, the velocity of the box after 10 seconds is 40 m/s.
To calculate the displacement over the 10s period, we can use the kinematic equation:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Given that the initial velocity is 0 m/s and the acceleration is 4 m/s^2, the equation simplifies to:
displacement = 0.5 * acceleration * time^2
displacement = 0.5 * 4 m/s^2 * (10s)^2
displacement = 200m
Therefore, the displacement of the box over the 10s period is 200 meters.
To find the acceleration of the box, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
1. In the first scenario, we have a force of 250N applied to the box and a frictional force of 195N opposing the motion. The net force is the difference between these two forces:
Net force = applied force - frictional force
Net force = 250N - 195N
Net force = 55N
Now, we can use Newton's second law to find the acceleration:
Acceleration = Net force / Mass
Acceleration = 55N / 60kg
Acceleration ≈ 0.92 m/s^2
Therefore, the acceleration of the box is approximately 0.92 m/s^2.
2. For the second scenario, the force applied is 40N, and the frictional force is 16N. The net force can be calculated similarly:
Net force = applied force - frictional force
Net force = 40N - 16N
Net force = 24N
Using Newton's second law, we find the acceleration:
Acceleration = Net force / Mass
Acceleration = 24N / 6kg
Acceleration = 4 m/s^2
To find the velocity of the box after 10 seconds, we can use the formula for constant acceleration:
Velocity = Initial velocity + (Acceleration * Time)
Since the initial velocity is zero (since the box was initially at rest), the equation becomes:
Velocity = 0 + (4 m/s^2 * 10s)
Velocity = 40 m/s
Therefore, the velocity of the box after 10 seconds is 40 m/s.
To calculate the displacement of the box over the 10-second period, we can use the equation:
Displacement = (Initial velocity * Time) + (0.5 * Acceleration * Time^2)
Since the initial velocity is zero, the equation simplifies to:
Displacement = 0 + (0.5 * 4 m/s^2 * (10s)^2)
Displacement = 0 + 0.5 * 4 m/s^2 * 100s^2
Displacement = 0 + 200 m
Displacement = 200 m
Therefore, the displacement of the box over the 10-second period is 200 meters.