kilograms is placed on the floor of an elevator. Neglect the mass of the platform scale. When the elevator is at rest, a man stands on the scale, which indicates 80 kg. Determine (a) the acceleration of the elevator when the scale indicates 100 kg; (b) the reading of the scale when the elevator has an acceleration of 4 mps 2 downward; and (c) the tension in the supporting cable for the elevator during the acceleration period if the total mass of the elevator, man and scale is 800 kg. (d) At what value of acceleration of the elevator would the person appear to be weightless? a R = 100 (9.8) = 980 N w = 80 (9.8) = 784 N y- axis
Transcript
A spring-operated platform scale which indicates mass in kilograms is placed on the floor of an elevator. Neglect the mass of the platform scale. When the elevator is at rest, a man stands on the scale, which indicates 80 kg. Determine (a) the acceleration of the elevator when the scale indicates 100 kg; (b) the reading of the scale when the elevator has an acceleration of 4 mps2 downward; and (c) the tension in the supporting cable for the elevator during the acceleration period if the total mass of the elevator, man and scale is 800 kg. (d) At what value of acceleration of the elevator would the person appear to be weightless?
a
R = 100 (9.8) = 980 N
w = 80 (9.8) = 784 N
y-axis
b) the reading of the scale when the elevator has an acceleration of 4 mps2 downward;
a = 4mps2
R = 100 (9.8) = 980 N
w = 80 (9.8) = 784 N
y-axis
c) the tension in the supporting cable for the elevator during the acceleration period if the total mass of the elevator, man and scale is 800 kg;
wT = 800 (9.8) = 7840N
y-axis
a = 4mps2
d) At what value of acceleration of the elevator would the person appear to be weightless
a
R = 0
w = 80 (9.8) = 784 N
y-axis
The coefficient of friction between the 35-kg block A and the plane in the figure is 0.50. Determine the acceleration of A under the action of the 100 N force when the velocity of A is , (a) 2.5 mps up the plane; and (b) 5 mps down the plane.
AP=100 N
3
4
AP=100 N
3
4N
W=35(9.8)=343 N
FK
aa)
x-axis
y-axis
AP=100 N
3
4N
W
FK
(b) 5 mps down the plane.
a
* The negative sign indicates that the body is decelerating and the correct direction of acceleration is UPWARD
x-axis
y-axis
Steps in solving problems in kinetics
1. Determine carefully hat data are given and hat is required in the problem.2. Draw the free-body diagram for each body involved in the problem. Indicate in
the diagram all the forces acting on the body. These forces ill include both the known applied forces acting on the particle, and the unknown reaction force exerted on the particle by the immediate supporting foundation which is imagined to be removed. Friction forces must always be directed to opposite relative motion.
3. In order to ensure that friction forces oppose the motion, determine the direction of motion if not evident or specified.
4. Determine the kinematic relations between the bodies involved in a connected system.
5. Select the x-axis as positive in the direction of the initial motion and apply ƩFx =max and ƩFy =0
6. Solve for the unknowns, using such additional equations of kinematics as may be required to determine the relations among displacement, velocity and time.
In the system of connected bodies as shown in the figure, the coefficient of kinetic friction is 0.25 under bodies B and C. Determine the acceleration of each body and the tension in the cord supporting A.
A
3
4NB
W = 400(9.8) = 3920 N
FKBaB
FBD of B:
FBD of A:
A
T
W
2T
WXB
3
4
NC
FKC
aC
T=1960 N
WXC
W = 600(9.8) = 5880 N
FBD of C:
Using kinematic relation using work method
(1)
For A:
For B:
For C:
(2)
(3)
(4)
Solving the system of equations, And then by substitution,
(3) & (1)
(5)
x -3 on (2) – (6)
(7)
x 3 on (1)
therefore,
(2)
The pulleys in the figure are frictionless and of negligible eight. Determine the tension in the cable supporting body C and the acceleration of each body.
200 kg
300 kg
150 kg
2T
aA
2T
aB
T
aC
200(9.8)=1960N 300(9.8)=2940N 150(9.8)=1470N
For A:For B:
For C:
Solving the system of equations, since
And then by substitution,
(1)
(2)
(3)
(4)
If blocks A and B of mass 10 kg and 6 kg, respectively, are placed on the inclined plane and released, determine the force developed in the link. The coefficientsof kinetic friction between the blocks and the inclined plane are μA = 0.1 and μB = 0.3. Neglect the mass of the link.
Determine the acceleration of the system and the tension in each cable. The inclined plane is smooth, and the coefficient of kinetic friction between the horizontal surface and block C is (μk)C = 0.2.
The sports car, having a mass of 1700 kg, travels horizontally along a 20° banked track which is circular and has a radius of curvature of ρ = 100 m . If the coefficient of static friction between the tires and the road is μ=0.2, determine the maximum constant speed at which the car can travel without sliding up the slope. Neglect the size of the car.
W=mg
N
an
20°
20°
Ff = μN
Determine the minimum coefficient of static friction between the tires and the road surface so that the 1.5-Mg car does not slide as it travels at 80 kmh on thecurved road. Neglect the size of the car.
an
ff
t
n
A 5-Mg airplane is flying at a constant speed of 350 km h along a horizontal circular path of radius , r=3000m . Determine the uplift force L acting on the airplane and the banking angle . Neglect the size of the airplane.
an
b
nW=5000kg (9.81 m/s2)=49,050 N
The 0.8-Mg car travels over the hill having the shape of a parabola. If the driver maintains a constant speed of 9 m s, determine both the resultant normal forceand the resultant frictional force that all the wheels of the car exert on the road at the instant it reaches point A. Neglect the size of the car.
