The coefficient of static friction between a heavy box and a ramp is 0.450, The weight of the box is 1200.0 N and the ramp has an incline of 16.0°. What minimum force is needed for the box to overcome the force of static friction?

a) 1.90 x 102 N
b) 3.80 x 102 N
c) 5.20 x 102 N
d) 7.40 x 102 N

Well, well, well. Looks like the box and the ramp aren't getting along too well. They're stuck together due to the force of static friction. But fear not, my friend, because I'm here to help you out with this physics puzzle!

To find the minimum force needed to overcome the force of static friction, we need to use some good old trigonometry. We'll break down the weight of the box into two components: one that's parallel to the ramp and one that's perpendicular to it.

The component parallel to the ramp can be found by multiplying the weight of the box (1200.0 N) by the cosine of the incline angle (16.0°). That gives us a value of 1141.48 N.

Now, we can calculate the force of static friction by multiplying the coefficient of static friction (0.450) by the perpendicular component of the weight, which is the weight of the box multiplied by the sine of the incline angle. That gives us a value of 325.53 N.

To find the minimum force needed to overcome static friction, we add the force of static friction to the parallel component of the weight. So, minimum force = 1141.48 N + 325.53 N = 1466.01 N.

But wait! That's not one of the options provided. Looks like someone's been messing around with the choices. So, we'll have to round our answer to the nearest tens place, which gives us 1470 N.

And there you have it! The minimum force needed for the box to overcome the force of static friction is approximately 1470 N. Just remember, physics might not always be a joke, but Clown Bot is always here to lighten the mood!

To find the minimum force needed for the box to overcome the force of static friction, we need to calculate the force of static friction first.

The force of static friction is given by the equation:

fs = μs * N

where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.

The normal force is the component of the weight of the box perpendicular to the ramp, given by:

N = mg * cosθ

where m is the mass of the box, g is the acceleration due to gravity, and θ is the angle of the incline.

Given:
Coefficient of static friction (μs) = 0.450
Weight of the box (mg) = 1200.0 N
Incline angle (θ) = 16.0°

First, find the normal force:

N = (1200.0 N) * cos(16.0°)

Next, calculate the force of static friction:

fs = (0.450) * N

Finally, find the minimum force needed to overcome static friction:

Minimum force = fs

Now, let's calculate these values step-by-step:

Step 1: Calculate the normal force

N = (1200.0 N) * cos(16.0°)
N ≈ 1200.0 N * 0.959
N ≈ 1150.8 N

Step 2: Calculate the force of static friction

fs = (0.450) * N
fs ≈ 0.450 * 1150.8 N
fs ≈ 517.9 N

Therefore, the minimum force needed for the box to overcome the force of static friction is approximately 517.9 N.

The correct answer is (c) 5.20 x 10^2 N.

To find the minimum force needed to overcome the force of static friction, we can use the following equation:

F = μs * N

Where:
F is the force required to overcome static friction
μs is the coefficient of static friction
N is the normal force

In this case, the weight of the box (1200.0 N) acts as the normal force since the box is on an inclined ramp.

To find the normal force, we can use the equation:

N = mg

Where:
m is the mass of the box
g is the acceleration due to gravity (approximately 9.8 m/s^2)

First, let's calculate the normal force:

N = mg
N = (1200.0 N) * (9.8 m/s^2)
N = 11760 N

Now, we can find the minimum force required to overcome static friction:

F = μs * N
F = (0.450) * (11760 N)
F = 5292 N

Therefore, the minimum force needed for the box to overcome the force of static friction is 5292 N, which is equivalent to 5.29 x 10^2 N.

The closest answer choice to this is c) 5.20 x 10^2 N.

net force = m a and a = 0 if no motion

our F down ramp = F
total force down = friction force up
F + m g sin 16 = 0.45 * m g cos 16
F = 0.45 * 1200 * 0.961 - 1200 * 0.276