a force F is applied in horizontal to a 10kg block. the block moves at a constant speed 2m/s across a horizontal surface. the coefficient of kinetic friction between the block and the surface is 0.5. the work done by the force F in 1.5 minutes is?
fn*m(coeffient of friction) = f(friction)
100*.5=50
Make velocity graph, convert 1.5min to seconds (60*1.5=90sec)
since constant, no acceleration
graph should look like rectangle v=2 on y axis t=90 on x axis
multiply like rectangle (2*90=180)
180 meters is the result
W=F*D
W=50 * 180
W=9000J
hope this helps <3
ggez
Well, well, well, let's see what we've got here. A force, a block, a coefficient of friction, and some work to be done. Sounds like a party!
Alright, here's the deal. We know the block is moving at a constant speed, which means that the force applied is perfectly balanced by the friction force. In other words, the force applied equals the force of friction.
The equation for friction is F_friction = μ * N, where F_friction is the force of friction, μ is the coefficient of kinetic friction, and N is the normal force acting on the block.
Since the block is moving horizontally, the normal force is equal to the gravitational force, which is given by N = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, the work done by a force is calculated using the equation W = F * d * cos(θ), where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and the direction of displacement.
In this case, the force is F_friction, the displacement is the distance traveled by the block (which is not given), and the angle between the force and the displacement is 0 degrees since they're both horizontal.
So, to find the work done, we first need to determine the force of friction. Using the equations I mentioned earlier, we have:
F_friction = μ * N = μ * (m * g)
Now, we need to find the displacement traveled by the block. You mentioned it moves at a constant speed of 2 m/s for 1.5 minutes. To make things easier, let's convert the time to seconds:
1.5 minutes = 1.5 * 60 = 90 seconds
So, we have a constant speed of 2 m/s for 90 seconds. We can calculate the distance traveled by multiplying the speed by the time:
Distance = Speed * Time = 2 m/s * 90 s = 180 meters
Now, we can use the equation for work to find the answer:
W = F_friction * d * cos(θ)
Plugging in the values we found:
W = (μ * (m * g)) * d * cos(0)
Since cos(0) = 1, we can simplify further:
W = μ * (m * g) * d
Now, we just need to plug in the given values:
W = 0.5 * (10 kg * 9.8 m/s^2) * 180 meters
And that, my friend, will give you the work done by the force F in 1.5 minutes. Go ahead and crunch those numbers, and remember to invite me to your next physics party!
To find the work done by force F, we need to know the formula for work and the distance over which the force is applied.
Work (W) is defined as the product of the force (F) acting on an object and the distance (d) over which the force is applied, and it can be calculated using the formula:
W = F × d × cos(θ)
Where:
- W is the work done (in joules, J)
- F is the magnitude of the force (in newtons, N)
- d is the distance over which the force is applied (in meters, m)
- θ is the angle between the direction of the force and the direction of the displacement
In this case, the force F is horizontal, so the angle θ between the force and displacement is 0 degrees. In this situation, the cosine of 0 degrees is 1, so we can simplify the formula to:
W = F × d
We are given the force F, which is not specified, but we know it must balance the force of kinetic friction acting on the block. Hence, our next step is to find the force of kinetic friction.
The force of kinetic friction (Fk) can be calculated using the equation:
Fk = μk × N
Where:
- Fk is the force of kinetic friction (in newtons, N)
- μk is the coefficient of kinetic friction
- N is the normal force
The normal force (N) is equal to the weight (mg) of the object, where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2).
N = mg
Given that the mass of the block (m) is 10 kg, the weight (N) is:
N = 10 kg × 9.8 m/s^2 = 98 N
Now, we can calculate the force of kinetic friction:
Fk = 0.5 × 98 N = 49 N
Since the block is moving at a constant speed, we know that the force applied (F) must be equal in magnitude and opposite in direction to the force of friction (Fk). Therefore, the force applied (F) is also 49 N.
Now, we need to find the distance (d) over which the force is applied. We are given the speed (v) of the block, which is 2 m/s, and the time (t) over which the force is applied, which is 1.5 minutes (90 seconds).
The distance (d) can be calculated using the formula:
d = v × t
d = 2 m/s × 90 s = 180 m
Finally, we can calculate the work done (W) by multiplying the force (F) by the distance (d):
W = F × d = 49 N × 180 m = 8820 J
Therefore, the work done by the force F in 1.5 minutes is 8820 joules.
work=force*distance
= 10*g*.5*2*1.5min*60sec/min