A block of mass 2.5 kg is pushed up against the vertical wall by a force of 60 N acting at 47◦ to the ceiling. The coefficient of kinetic friction between the block and the wall is 0.67. The acceleration of gravity is 9.8 m/s2 . Find the work done by this force in moving the block upward by a distance 1.5 m. Answer in units of J
Well, this situation sounds pretty "uplifting." Let's solve it together!
To find the work done by the force in moving the block upward, we need to calculate the product of the force applied and the distance moved in the direction of the force. So, let's break it down step by step.
First, we need to find the component of the force that acts parallel to the displacement. The force applied at 47 degrees to the ceiling can be split into two components: one parallel to the wall and the other perpendicular to it.
The component of the force parallel to the wall can be calculated using trigonometry:
Force parallel = Force applied * cos(47 degrees)
Plugging in the values, we get:
Force parallel = 60 N * cos(47 degrees)
Next, we can calculate the frictional force acting against the motion of the block. The frictional force can be found using the equation:
Frictional force = coefficient of kinetic friction * normal force
The normal force is equal to the weight of the block:
Normal force = mass * acceleration due to gravity
Normal force = 2.5 kg * 9.8 m/s^2
Now we can calculate the frictional force:
Frictional force = 0.67 * (2.5 kg * 9.8 m/s^2)
Finally, we can determine the net force acting on the block by subtracting the frictional force from the component of the force parallel to the wall:
Net force = Force parallel - Frictional force
Now, we can calculate the work done by multiplying the net force by the distance moved in the direction of the force:
Work done = Net force * distance
Work done = (Net force) * 1.5 m
After performing the calculations, you should get the answer in units of joules (J).
And there you have it! Just remember to keep your spirits high, even when you're dealing with physics problems.
To find the work done by the force in moving the block upward, we can use the equation:
Work = Force x Distance x Cosine(angle)
Given:
Mass of the block (m) = 2.5 kg
Force (F) = 60 N
Angle (θ) = 47 degrees
Coefficient of kinetic friction (μ) = 0.67
Distance (d) = 1.5 m
Acceleration due to gravity (g) = 9.8 m/s^2
First, let's find the normal force (N) acting on the block due to its weight:
Weight of the block (W) = m x g
W = 2.5 kg x 9.8 m/s^2
Since the block is pushed against the wall, the normal force is equal to the weight of the block:
N = 2.5 kg x 9.8 m/s^2
Next, let's find the frictional force (f) opposing the motion of the block:
Frictional force (f) = μ x N
f = 0.67 x (2.5 kg x 9.8 m/s^2)
Next, let's find the net force (F_net) acting on the block:
F_net = F - f
F_net = 60 N - (0.67 x 2.5 kg x 9.8 m/s^2)
Now, let's find the acceleration (a) of the block using Newton's second law:
F_net = m x a
a = F_net / m
Finally, let's find the work done by the force:
Work = F x d x cos(θ)
Work = (F_net / m) x d x cos(θ)
Now, substituting the given values into the equation:
Work = [((60 N - (0.67 x 2.5 kg x 9.8 m/s^2)) / 2.5 kg) x 1.5 m x cos(47°)]
Calculating this expression will give you the work done by the force in moving the block upward by a distance of 1.5 m.
To find the work done by the force in moving the block upward, we need to calculate the displacement of the block and then multiply it by the force applied.
First, let's break down the given information:
Mass of the block (m) = 2.5 kg
Force applied (F) = 60 N
Angle between the force and the vertical wall (θ) = 47◦
Coefficient of kinetic friction (μ) = 0.67
Acceleration due to gravity (g) = 9.8 m/s^2
Distance moved upward (d) = 1.5 m
Since the force is acting at an angle to the ceiling, we need to find the component of the force that is parallel to the displacement. In this case, it is the force component acting upward.
The vertical component of the force (Fy) can be found using trigonometry:
Fy = F * sin(θ)
Fy = 60 N * sin(47◦)
Next, we need to find the frictional force (f) opposing the motion of the block. The frictional force can be calculated using the equation:
f = μ * (normal force)
The normal force (N) is the force exerted by the wall perpendicular to the surface of the block. Since the block is pushed against the wall, the normal force is equal to the weight of the block:
N = m * g
The frictional force can now be calculated using the formula:
f = μ * N
f = 0.67 * (2.5 kg * 9.8 m/s^2)
Now we can determine the net force (Fnet) acting on the block:
Fnet = Fy - f
Finally, we can calculate the work done by the force (W) using the formula:
W = Fnet * d
Substituting the values into the equation, we can now calculate the work done.