A 20 g fridge magnet is being held onto the fridge by a 0.9 N force. coefficient of kinetic friction is 0.3 . (please include an FBD when giving the solutions)
a. calculate the friction acting on the magnet.
b. calculate the weight of the magnet
c.the acceleration of the magnet.
please explain along the way
First, let's draw the Free Body Diagram (FBD) of the forces acting on the fridge magnet.
There are three main forces acting on the magnet.
1. The gravitational force (weight) acting vertically downwards, denoted as W.
2. The force holding the magnet onto the fridge, acting vertically upwards, denoted as F (given as 0.9 N).
3. The frictional force acting horizontally to oppose the motion of the magnet, denoted as F_friction.
The gravitational force (W) can be calculated as:
W = m * g
where m is the mass of the magnet (0.020 kg, converted from 20g) and g is the acceleration due to gravity (approximately 9.81 m/s^2).
W = 0.020 * 9.81 = 0.1962 N
Now that we have the weight of the magnet, we can move on to part (a).
a) Calculate the friction acting on the magnet.
To find the frictional force, we need to use the formula:
F_friction = μ * N
where μ is the coefficient of kinetic friction (0.3) and N is the normal force.
In this case, the normal force (force perpendicular to the surface) is equal to the force holding the magnet onto the fridge (the 0.9 N force). This is because the magnet is in equilibrium in the vertical direction (it's not moving up or down).
F_friction = 0.3 * 0.9 = 0.27 N
For part (b), we already calculated the weight of the magnet above:
The weight of the magnet, W = 0.1962 N.
For part (c), we need to find the acceleration of the magnet.
As the magnet is in equilibrium in the vertical direction, we only need to consider forces in the horizontal direction. Newton's second law states that:
F_net = m * a,
where F_net is the net force acting on the object, m is the mass, and a is the acceleration.
Since the only force acting horizontally is the frictional force, and it is opposing the direction of the movement of the magnet:
F_net = -F_friction = -0.27 N
Now we can calculate the acceleration:
a = F_net / m = -0.27 / 0.020 = -13.5 m/s²
The acceleration of the magnet is -13.5 m/s², indicating that it is decelerating due to the frictional force.
In summary,
a) The frictional force acting on the magnet is 0.27 N.
b) The weight of the magnet is 0.1962 N.
c) The acceleration of the magnet is -13.5 m/s².
Sure! Let's go step by step to solve each part of the problem:
a. To calculate the friction acting on the magnet, we need to use the formula for frictional force:
Frictional force = coefficient of kinetic friction × normal force
The normal force is the force exerted by the surface perpendicular to the direction of motion. In this case, the normal force is equal to the weight of the magnet (since there is no vertical acceleration). So, to find the frictional force, we need to find the weight of the magnet first.
b. The weight of an object is given by the formula:
Weight = mass × acceleration due to gravity
Given that the mass of the magnet is 20 grams (or 0.02 kg) and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight.
c. Once we have the weight of the magnet, we can calculate the net force acting on it. The net force is given by:
Net force = applied force - frictional force
Since the magnet is being held onto the fridge with a force of 0.9 N and the frictional force is acting in the opposite direction, we can substitute these values and calculate the net force.
Now, we can use Newton's second law to find the acceleration of the magnet:
Net force = mass × acceleration
We have the net force from the previous step and the mass of the magnet, so we can substitute these values and solve for the acceleration.
Now, let's summarize the solutions step by step:
a. Solution:
- Frictional force = coefficient of kinetic friction × normal force
b. Solution:
- Weight = mass × acceleration due to gravity
c. Solution:
- Net force = applied force - frictional force
- Net force = mass × acceleration
By following these steps, you should be able to calculate the frictional force, weight, and acceleration of the magnet.
Sure! Let's go step by step to find the solutions to each part of the problem.
a. To calculate the friction acting on the magnet, we first need to find the normal force exerted on the magnet by the fridge. The normal force is equal in magnitude but opposite in direction to the force exerted by the magnet on the fridge, which is 0.9 N. So, the normal force is also 0.9 N.
Now, we can calculate the frictional force using the formula: Frictional force (Ffr) = coefficient of kinetic friction (μk) × Normal force (N).
Given that the coefficient of kinetic friction (μk) is 0.3 and the normal force (N) is 0.9 N, we can plug these values into the formula:
Ffr = 0.3 × 0.9
Ffr = 0.27 N
Therefore, the friction acting on the magnet is 0.27 N.
b. To calculate the weight of the magnet, we can use the formula: Weight (W) = mass (m) × acceleration due to gravity (g).
The mass of the magnet is given as 20 g, which means we need to convert it to kilograms by dividing it by 1000:
20 g ÷ 1000 = 0.02 kg.
The acceleration due to gravity is approximately 9.8 m/s².
Now we can find the weight by multiplying the mass and acceleration due to gravity:
W = 0.02 kg × 9.8 m/s²
W = 0.196 N
So, the weight of the magnet is approximately 0.196 N.
c. To calculate the acceleration of the magnet, 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: Net force (Fnet) = mass (m) × acceleration (a).
In this case, the net force is the force exerted by the magnet on the fridge minus the frictional force:
Fnet = 0.9 N - 0.27 N
Fnet = 0.63 N
The mass of the magnet is 0.02 kg (as calculated in part b).
Now we can find the acceleration by rearranging the formula:
Fnet = m × a
0.63 N = 0.02 kg × a
Divide both sides of the equation by 0.02 kg to solve for acceleration:
a = 0.63 N ÷ 0.02 kg
a = 31.5 m/s²
Therefore, the acceleration of the magnet is 31.5 m/s².
Here is the free-body diagram (FBD) of the forces acting on the magnet:
- The force exerted by the magnet on the fridge (Fapplied) is 0.9 N.
- The frictional force (Ffr) is 0.27 N, acting opposite to the applied force.
- The weight of the magnet (W) is 0.196 N, acting downward.
- The normal force (N) is equal in magnitude but opposite in direction to the applied force (0.9 N).
FBD:
← Fapplied (0.9 N) ← Ffr (0.27 N)
---------------------------------------------
→ N (0.9 N) →
---------------------------------------------
↑ ↓
W (0.196 N) →
I hope this explanation helps! Let me know if you have any further questions.