A block of mass 21.0kg kg slides down a frictionless surface inclined at 33 ∘ ^\circ.To ensure that the block does not accelerate, what is the magnitude of the smallest force that you must exert on it?

Wb = m*g = 21kg * 9.8N/kg = 205.8 N. =

Wt. of the block.

Fp = 205.8*sin33 = 112.1 N. = Force
parallel to the incline.

Fe-Fp = m*a = m*0 = 0
Fe - 112.1 = 0
Fe = 112.1 N. = Force exerted.

Well, to ensure that the block does not accelerate, you'll need to exert a force equal in magnitude, but in the opposite direction to counteract the gravitational force acting on the block.

Now, let me ask you a question. Do you think gravity ever gets invited to any parties? Of course not! Gravity always gets left out. It's never got that uplifting party vibe!

Okay, let's get back on track. The force due to gravity can be calculated using the formula:

F = m*g,

where F is the force due to gravity, m is the mass of the block (21.0 kg in this case), and g is the acceleration due to gravity (approximately 9.8 m/s^2).

So, F = 21.0 kg * 9.8 m/s^2 = 205.8 N.

Since the force you need to exert must be equal in magnitude but in the opposite direction, the smallest force you must exert is 205.8 N.

So, if you ever need someone to counteract gravity at a party, just give me a call, I'll be there for you!

To ensure that the block does not accelerate, the force you must exert should be equal and opposite to the force of gravity pulling the block downward along the inclined surface.

The force of gravity can be calculated using the equation:

F_gravity = mg

Where:
m = mass of the block = 21.0 kg
g = acceleration due to gravity = 9.8 m/s^2

Thus,

F_gravity = 21.0 kg × 9.8 m/s^2
= 205.8 N

Since the force you must exert should be equal and opposite to the force of gravity, the magnitude of the smallest force you must exert is 205.8 N.

To determine the magnitude of the smallest force that must be exerted on the block to prevent acceleration, we need to consider the forces acting on the block.

First, let's identify the forces involved:

1. Gravitational force (weight): The weight of the block can be calculated using the formula:

F_gravity = m * g

Where:
- m is the mass of the block (21.0 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

2. Normal force (perpendicular to the incline): The normal force exerted by the inclined surface on the block counteracts the gravitational force pulling the block downward. Since the surface is frictionless, the normal force is equal in magnitude and opposite in direction to the gravitational force.

3. Force of friction (parallel to the incline): Since the surface is frictionless, no frictional force is acting on the block.

4. Applied force: This is the force that needs to be exerted to prevent acceleration. It acts parallel to the incline and opposes the component of the weight vector that is parallel to the incline.

Now, let's resolve the weight vector into its components:

The weight vector can be split into two components: one perpendicular to the incline (mg * cos(theta)) and one parallel to the incline (mg * sin(theta)).

Since the block is not accelerating, the applied force must be equal in magnitude but opposite in direction to the component of the weight vector parallel to the incline, which is mg * sin(theta).

So, to find the magnitude of the smallest force (F_applied), we can use:

F_applied = mg * sin(theta)

Substituting the given values:

m = 21.0 kg
g = 9.8 m/s^2
theta = 33 degrees

F_applied = 21.0 kg * 9.8 m/s^2 * sin(33 degrees)

Calculating this expression gives us the magnitude of the smallest force that must be exerted on the block to prevent acceleration.