A dockworker applies a constant horizontal force of 79.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves a distance 13.0 m in a time 4.50 s. What is the mass of the block of ice?If the worker stops pushing at the end of 4.50 s, how far does the block move in the next 4.70 s?
F=ma
79=m*a
but you can find a from
d=1/2 a t^2, you are given d, and t.
61.7
To find the mass of the block of ice, 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.
Given:
Applied force (F) = 79.0 N
Distance (d) = 13.0 m
Time (t) = 4.50 s
To find the mass (m) of the block, we need to find its acceleration (a) first.
Step 1: Calculate the acceleration (a):
We can use the displacement equation, which states that displacement (d) is equal to initial velocity (v0) multiplied by time (t) plus one-half the acceleration (a) multiplied by the square of time (t).
d = v0 * t + (1/2) * a * t^2
Since the block starts from rest, the initial velocity (v0) is 0.
0 = 0 * 4.50 + (1/2) * a * (4.50)^2
0 = 0 + 2.25a * 20.25
0 = 45.56a
a = 0 m/s^2
Step 2: Calculate the mass (m):
Since acceleration (a) is 0 m/s^2, the block is not accelerating, which means the net force acting on it is also 0.
The applied force (F) is the only force acting on the block, which means it must be balanced by the force of static friction.
F = static friction (fs)
fs = F
Since the force of static friction is equal to the force applied, we can use the equation:
fs = μs * N
where μs is the coefficient of static friction and N is the normal force.
Since the frictional force is negligible, we can assume that the coefficient of static friction (μs) is 0.
fs = 0 * N = 0 N
Therefore, the applied force (F) is also 0 N.
Now, we can calculate the mass (m) by rearranging Newton's second law of motion equation:
F = m * a
m = F / a = 0 N / 0 m/s^2
The mass of the block of ice cannot be determined with the given information because the block does not experience any acceleration.
To find how far the block moves in the next 4.70 seconds, we need to use the equations of motion.
Since the block is at rest after 4.50 seconds, its final velocity (v) is 0 m/s.
v = v0 + at
0 = v0 + 0 * 4.70
v0 = 0 m/s
Using the equation for displacement:
d = v0 * t + (1/2) * a * t^2
d = 0 * 4.70 + (1/2) * 0 * (4.70)^2
d = 0 m
Therefore, the block does not move any further in the next 4.70 seconds after the worker stops pushing it.
To find the mass of the block of ice, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:
F = m * a
In this case, the force applied by the dockworker is given as 79.0 N, and the acceleration can be calculated using the kinematic equation:
d = v0 * t + (1/2) * a * t^2
Where:
d is the distance traveled (13.0 m),
v0 is the initial velocity (0 m/s),
t is the time (4.50 s).
We can rearrange the equation to solve for acceleration (a):
a = (2 * d - v0 * t) / t^2
Substituting the given values, we have:
a = (2 * 13.0 m - 0 m/s * 4.50 s) / (4.50 s)^2
a = (26.0 m) / (20.25 s^2)
a ≈ 1.28 m/s^2
Now, we can use this acceleration and the applied force to find the mass (m) of the block of ice:
79.0 N = m * 1.28 m/s^2
Solving for m:
m = 79.0 N / 1.28 m/s^2
m ≈ 61.72 kg
Therefore, the mass of the block of ice is approximately 61.72 kg.
Now, let's find out how far the block of ice moves in the next 4.70 s after the worker stops pushing. Since there is no external force acting on the block after the worker stops pushing, the block's velocity remains constant.
We can use the formula:
d = v * t
Where:
d is the distance traveled,
v is the constant velocity,
t is the time (4.70 s).
However, we need to determine the constant velocity of the block after the worker stops pushing. We can do this by using the equation:
v = v0 + a * t
Where:
v0 is the final velocity at the end of 4.50 s (calculated from the previous information),
a is the acceleration (calculated above),
t is the time interval being considered (4.70 s).
Substituting the given values:
v = 0 m/s + 1.28 m/s^2 * 4.50 s
v ≈ 5.76 m/s
Now, we can calculate the distance traveled (d) using the formula:
d = v * t
Substituting the values:
d = 5.76 m/s * 4.70 s
d ≈ 27.07 m
Therefore, the block of ice moves approximately 27.07 meters in the next 4.70 seconds after the worker stops pushing.