2. a body of mass 20kg is released from rest t the top of a rough slope which is inclined at 30 degrees to the horizontal.six seconds later the body has a velocity of 21 m.s down the slope. find the resistance to motion in newtons experienced by the body?
Fb=mg = 20kg * 9.8N/kg = 196N @ 30deg.
Fp = 196*sin30 = 98N = Force parallel
to plane.
a=(Vf-Vo) / t = (21-0) / 6 = 3.5m/s^2.
Fn = Fp-Ff = ma,
98 - Ff = 20 * 3.5,
Ff = 28N = Force of friction.
To find the resistance to motion experienced by the body, we need to calculate the force acting on the body along the slope.
Step 1: Find the gravitational force acting on the body.
The gravitational force acting on the body can be calculated using the formula:
Weight = mass × acceleration due to gravity
where acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 20 kg × 9.8 m/s^2 = 196 N
Step 2: Resolve the weight of the body into components.
We need to resolve the weight of the body into two components: one parallel to the slope and one perpendicular to the slope.
Parallel component (Fp) = Weight × sin(angle of inclination)
Fp = 196 N × sin(30 degrees) = 196 N × 0.5 = 98 N
Perpendicular component (Fn) = Weight × cos(angle of inclination)
Fn = 196 N × cos(30 degrees) = 196 N × 0.866 = 169.936 N (approximately 170 N)
Step 3: Calculate the net force acting on the body.
The net force acting on the body is the difference between the parallel component of the weight and the resistance force.
Net force = Fp - resistance force
Step 4: Find the acceleration of the body.
Using the equation of motion: v = u + at, where
v = final velocity (21 m/s),
u = initial velocity (0 m/s),
t = time (6 s)
Rearranging the equation, we have:
a = (v - u) / t = (21 m/s - 0 m/s) / 6 s = 3.5 m/s^2
Step 5: Calculate the resistance force using Newton's second law of motion.
Using Newton's second law, F = ma, where
F = net force,
m = mass,
a = acceleration
Resolving forces along the slope, the equation becomes:
Fp - Resistance force = mass × acceleration
98 N - Resistance force = 20 kg × 3.5 m/s^2
Step 6: Solve for the resistance force.
Resistance force = 98 N - (20 kg × 3.5 m/s^2)
Resistance force = 98 N - 70 N
Resistance force = 28 N
Therefore, the resistance to motion experienced by the body is 28 Newtons.
To find the resistance to motion experienced by the body, we first need to calculate the acceleration of the body down the slope. We can then use Newton's second law of motion to find the resistance.
Step 1: Calculate the acceleration of the body down the slope.
The acceleration of the body down the slope can be calculated using the following formula:
acceleration = (velocity_final - velocity_initial) / time
Here, the initial velocity (velocity_initial) is 0 m/s, the final velocity (velocity_final) is 21 m/s, and the time (time) is 6 seconds.
acceleration = (21 m/s - 0 m/s) / 6 s = 3.5 m/s^2
Step 2: Calculate the resistance to motion.
According to Newton's second law of motion, the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a).
force = mass × acceleration
Here, the mass (m) is given as 20 kg and the acceleration (a) is calculated as 3.5 m/s^2.
force = 20 kg × 3.5 m/s^2 = 70 N
Therefore, the resistance to motion experienced by the body is 70 Newtons.