physics problem! please help?
A block of mass m1 = 4.40 kg on a frictionless inclined plane of angle 30.0° is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.60 kg hanging vertically.
(a) What is the magnitude of the acceleration of each block?
(b) What is the direction of the acceleration of m2?
answer: m2 accelerates downwards
(c) What is the magnitude of the tension in the cord?
Comments
There are two sets of answers depending upon whether the plane is inclined upwards or downwards from the pulley.
Assume acceleration due to gravity (g) is 9.8 m/s^2.
Gravitational force on m1 providing acceleration to the system
= 4.40 * Sin(30) * g
= 21.56 N
Gravitational force on m2 providing acceleration to the system
= 2.60 * g
= 25.48 N
Total mass to be accelerated
= 4.4 + 2.6
= 7.0 kg
If the plane slopes down from the pulley, the effective force accelerating the system
= 25.48 - 21.56
= 3.92 N
a)
Acceleration of the blocks
3.92 = 7.0 * a
a = 3.92 / 7.0
= 0.56 m/s^2
b)
acceleration of m2 will be downwards
c)
m2 is accelerating at 0.56 m/s^2
Force accelerating m2
= 0.56 * 2.60
= 1.456 N
Tension in the cord
= 25.48 - 1.456
= 24.024 N
If the plane slopes upwards from the pulley, the effective force accelerating the system
= 25.48 + 21.56
= 47.04 N
a)
Acceleration of the blocks
47.04 = 7.0 * a
a = 47.04 / 7.0
= 6.72 m/s^2
b)
Acceleration of m2 is downwards
c)
Force accelerating m2
= 6.72 * 2.60
= 17.472 N
Tension in the cord
= 25.48 - 17.472
= 8.008 N
First a bit of physics. Because the whole thing is frictionless, we can consider the entire system to be suspended in the air so that it looks like:
o
| \
| \
|....[] 4.4
[]
2.6
a) Clearly, as they are attached by the cord, both blocks will accelerate at the same rate; otherwise, the cord would snap. The net force f = (m1 + m2)A = W1 - W2 sin(theta) = g (m1 - m2 sin(theta)) so that the acceleration is A = g (m1 - m2 sin(theta))/(m1 + m2) = 9.8*(2.6 - 4.4*sin(30))/(7) = 0.56 m/s^2. ANS.
b) As W2 sin(theta) has a minus sign, the force and therefore the acceleration due to gravity on the block is down slope. But, this is important, that is not the net acceleration, A. A is up slope. That should be obvious from the diagram. ANS. m2 is not...not...accelerating down slope, if it were the cord would snap. What's down slope is the effective acceleration due to gravity which is not A.
c) W1 = m1 g = 2.6*9.8 = 25.48 N and w2 = W2 sin(30) = m2 g sin(30) = 2.2*9.8 = 21.56 N; so the tension on the cord is 21.56 N. ANS.