A solid uniform ball of mass 1.0 kg and radius 1.0 cm starts from rest and rolls down a 1.0-m high ramp. There is enough friction on the ramp to prevent the ball from slipping as it rolls down
(a) What is the forward speed of the ball when it reaches the bottom of the ramp?
(b) What would be the forward speed of the ball if there were no friction on the ramp?
(c) Since the ball starts from the same height in both cases, why is the speed different?
(a) 3.7 m/s (b) 4.4 m/s
(c) With friction, some of the initial potential energy goes into rotational kinetic energy, leaving less for translational kinetic energy. Without friction, the ball does not rotate, so all the initial potential energy goes into translational kinetic energy.
You might also like to view...
A long, 2-cm-diameter horizontal copper pipe carries dry saturated steam at 120 kPa absolute pressure. The pipe is contained within an environmental testing chamber in which the ambient air pressure can be adjusted from 50 kPa to 200 kPa absolute, while the ambient air temperature is held constant at 20°C. What is the effect of this pressure change on the rate of condensate flow per meter length of pipe? Assume that the pressure change does not affect the absolute viscosity, thermal conductivity, or specific heat of the air.
GIVEN
• A long horizontal copper pipe carrying saturated steam within an environmental testing chamber
• Outside diameter (D) = 2 cm = 0.02 m
• Steam pressure = 120 kPa
• Ambient pressure range (P) = 50 to 200 kPa
• Ambient air temperature (T?) = 20°C FIND
• Effect of ambient pressure change on rate of condensate flow per meter length of pipe
ASSUMPTIONS
• Pressure change has no effect on absolute viscosity, thermal conductivity, or specific heat of the air
• Air is still
• Chamber temperature is held constant while pressure is changed
• Convective thermal resistance on the inside of the pipe is negligible
• Thermal resistance of the copper pipe is negligible
• The air behaves as an ideal gas
SKETCH
PROPERTIES AND CONSTANTS
For saturated steam 0.12 MPa the heat of vaporization (hfg) = 2238 kJ/kg, and the temperature (Ts) = 105°C.
for dry air at the mean temperature of 62.5°C and one atmosphere
Thermal expansion coefficient (?) = 0.00298 1/K
Thermal conductivity (k) = 0.0281 W/(m K)
Absolute viscosity (?) = 20.02 × 10–6 (N s)/m2
Prandtl number (Pr) = 0.71
Density (?) = 1.018 kg/m3
For an ideal gas 12PP = 12
Earth has been gradually warming in recent decades, and very strong evidence indicates that the cause of this warming is
A) human activities that are increasing the concentration of greenhouse gases in Earth's atmosphere. B) the increase in forest fires during recent years. C) a gradual brightening of the Sun. D) the fact that our politicians spout a lot of hot air.
This diagram represents an edge-on view of our Milky Way Galaxy. Of the four labeled points, which one could represent the Sun's position in the galaxy?
A) point 1 B) point 2 C) point 3 D) point 4
Top of the saturated zone
What will be an ideal response?